91Ó°ÊÓ

Locate the centre of mass of a uniform straight rod of mass \(m\) and length \(L\).

Statement-1: Linear momentum of a system of particles with respect to centre of mass must be zero. Statement-2: Linear momentum of a system of particles is the vector-sum of linear momenta of all particles of the system.

A ball of mass \(m\) moving at a speed \(v\) makes a head on collision with an identical ball at rest. 'The kinetic energy of balls after the collision is \(\frac{3}{4} t h\) of the original. If \(e\) is the coefficient of restitution. Then: (a) \(v_{1}-\frac{1 \times \frac{1}{\sqrt{2}}}{2} v\) (b) \(v_{2}-\frac{1-\frac{1}{\sqrt{2}}}{2} v\) (c) \(e-\frac{1}{\sqrt{2}}\) (d) \(e-\frac{1}{2}\)

A ball of mass \(M\) strikes another ball of mass \(m\) at rest. If they separate in mutually perpendicular directions, then the coefficient of impact (e) is (a) \(\frac{M}{m}\) (b) \(\frac{m}{M}\) (c) \(\frac{m}{2 M}\) (d) Zero

A loaded spring gun of mass \(M\) fires a shot of mass \(m\) with a velocity \(v\) at an angle of elevation \(\theta\). The gun is initially at rest on a horizontal frictionless surface. After firing the centre of mass of the gun- shot system (a) Moves with a velocity \(\frac{\mathrm{v} m}{M}\) (b) Moves with a velocity \(\frac{v m}{M \cos 0}\) in the horizontal direction (c) Moves with a velocity \(\frac{m v \sin \theta}{M+m}\) along vertical (d) Moves with velocity \(v(M-m) /(M+m)\) in horizontal direction

A uniform metal rod of length \(1 \mathrm{~m}\) is bent at \(90^{\circ}\) so as to form two arms of equal length. The centre of mass of this bent rod is (a) on the bisector of the angle, \(\left(\frac{1}{\sqrt{2}}\right) \mathrm{m}\) from vertex (b) on the bisector of the angle, \(\left(\frac{1}{2 \sqrt{2}}\right) \mathrm{m}\) from vertex (c) on the bisector of the angle, \(\left(\frac{1}{2}\right) \mathrm{m}\) from vertex (d) on the bisector of the angle, \(\left(\frac{1}{4 \sqrt{2}}\right)\) m from vertex

Two stars of masses \(M\) and \(m, M\) being greater than \(m\) are separated by a distance \(D .\) At a point between the two stars, their gravitational fields are equal in magnitude but opposite in direction. At that point a test object will feel no force. This point is: (a) At the c,m, of the two-star system (b) Between the c.m. and the mid point between the two stars (c) Between the c.m. and the star of Mass \(M\) (d) Between the mid-point of the two stars and the star of mass \(m\)